| Summary: | 碩士 === 臺灣大學 === 土木工程學研究所 === 98 === SCM(Spline Collocation Method) is a numerical analysis method originating from Spline function which is derived from Forward Difference, and also joining the idea of knot-collocating together. By means of developing B Spline Value Table from differential Spline function in various orders, the calculating process can be simplified greatly by simply looking up to the table. Furthermore, it can be used in computer programming in a systematic way. Therefore it becomes much more rapid and convenient when analyzing by using SCM.
The purpose of this thesis is to apply MSCM(Modified Spline Collocation Method) which is extended from SCM (Spline Collocation Method) to solve free vibrating problem of single-walled carbon nanotubes to obtain the natural frequency of the system being analyzed. Also, by leading in different combinations of boundary conditions, increasing the numbers of knots, observe the vibrating frequency and corresponding model shape. As for carbon nanotubes, it is clearly illustrated in this thesis that it is a perfect material for the development of ultrahigh frequency sensors, actuators and resonators due to exceptionally high stiffness, high strength and large aspect ratio.
At last, results from each example analyzed by SCM will be utilized to compare with theoretical solution derived from Euler-Bernoulli beam model and analytic solution by using other numerical method. Thus it can be verified that the error conducted by SCM is within the standard range of engineering field. It is demonstrated that SCM has its superiority as being one kind of accurate, fast, convenient and applicable numerical method; hence it is indeed worth doing further research.
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